Towards a Hub-ad-Spoke Network: a Study o the Chiese Mailad Hub Airport Plaig ZOU Bo,, LU Huapu, LIU Qiag Istitute of Trasportatio Egieerig, Tsighua Uiersity, Beijig, 00084, Chia Ecole Cetrale de Nates, Nates, 443, Frace Abstract: The airlies reorgaizatio will accelerate the switch of the Chiese mailad ciil aiatio system from a former poit-to-poit (PP) structure to a hub-ad-spoke (HS) etwork. I such a cotext, the major efforts of our paper are put ito idetifyig hub airports i mailad Chia. We first aalyze the HS etwork s competitie adatages ad fid four desirable hub characteristics. A three-leel method is deeloped to icorporate the required hub features ad applied to the hub airport plaig. Roles of the hubs i the plaig scheme are maily i three categories. Further discussio is exteded to etwork adjustmet as well as its dyamic eolutio. Key Words: HS etwork; PP structure; hub airport plaig; Chiese mailad Itroductio The airlies reorgaizatio i mailad Chia completed i Oct. 00 is a key step i the switch from a former poit-to-poit-domiat structure to a hub-ad-spoke (HS) etwork. More tha twety domestic airlies hae merged ito three groups: Air Chia, Chia Easter, ad Chia Souther. I additio, Haia airlies, a regioal airlie before, became the fourth largest passeger air carrier by combig seeral of its former rials. Meawhile, airlies hae more freedom to recofigure their routes. Most airlies choose to adopt the HS system, which is most popular amog worldwide top 0 airlies. Related research bega i the mid 980s i the wester world; early researchers iclude Kaafai ad Ghobrial (985), Morriso ad Wisto (986), ad Oum ad Tretheway (987), who hae idetified this pheomeo ad offered explaatios for the icrease i HS routig i the era of deregulatio. To address hub airport selectio issue, the ucapacitated sigle allocatio p-hub media problem was first proposed by O Kelly (987), followed by T. Ayki (990) ad J. G. Klicewicz (99). Further deelopmet of the models were made by J. F. Campbell (996), ad T. Erst ad M. Krishamoorthy (996 ad 998). These models are, howeer, usually mathematically difficult to sole; moreoer, may approximatios i them reder the results sometimes far away from reality. Releat study of the HS etwork is comparatiely less i mailad Chia, which could be attributed to the fact that the airlie idustry etwork i Chia still to some extet remais i a poit-to-poit (PP) form. Zhag (000) discussed some prerequisites of the operatio of a HS system. Ji (00 ad 005) gae a oeriew of the coutry s passeger airlie etwork deelopmet of the past two decades ad costructed a ideal etwork orgaizatio model. I his research the hub airports were selected based o a idex ealuatio system i which weights were predetermied i a quite subjectie maer. Bai (006) proided a method icludig hub selectio ad mai routes desig. Howeer, the results of the first part were obtaied through a similar idex ealuatio process which oly cosiders the local features, e.g. airport operatios.
The recet emergece of complex etwork has shed some lights o the aiatio etwork research. It has bee foud that HS structure is a prime example of a small-world etwork (L. A. Schitler 00). Ioled i this area are primarily physicists, amog which R. Guimera ad L. A. N. Amaral (004) studied the world airports system ad cocluded that it embodies the small world properties; Cai et al. ad Gaesh Bagler did some statistical research of Chiese ad U.S., ad Idia airport system respectiely ad foud similar results. Their outcomes, howeer, are maily focused o the etwork s mathematical ad statistical properties. No suggestios are see to our kowledge i practical terms while applyig the complex etwork theories to aiatio etwork study. To fill these gaps, a attempt is made i our paper to determie hub airports i the mailad Chia i the cotext of a HS structure. The rest of the paper is orgaized as follows: i sectio we aalyze the competitie adatages of such structure by comparig it with a PP etwork. Hub characteristics are subsequetly deried. After explorig the curret Chiese mailad airport system ad its problems i sectio 3, a three-leel method icorporatig the aboe desirable hub characteristics is gie ad applied to fidig out hub airports i sectio 4. Further implicatios are discussed i the followig sectio which icludes etwork adjustmet ad dyamic eolutio. I the ed, coclusios are gie ad further studies are directed. Aalysis of HS Aiatio Network. Competitie Adatages of HS Aiatio Network A typical HS strategy is that all passegers departig from ay o-hub origi to other cities i the etwork proceed first to the hub. Similarly, all passegers traelig to o-hub destiatios arrie at those destiatios from the hub. I order to uderstad the competitie adatages of the HS system oer its PP couterpart, we start with a simple case which cotais 9 airports. Uder the PP structure, a miimum of 7 flights ad 36 aircrafts are eeded; if it is trasformed ito a HS system with 3 hubs, howeer, a miimum of oly 8 flights ad 9 aircrafts are required. The reductio is sigificat, ad therefore would cosiderably sae operatios costs for airlies. I additio, cost adatages are also gaied by creatig the ecoomy of desity which maifests itself maily i two parts. First, the cosolidatio of passegers from may routes o a sigle spoke icrease the desity of serice alog each spoke. Although hubbig eed ot chage which airports a airlie seres or the umber of passegers it trasports, hubbig does decrease the umber of routes o which a airlie operates its plaes ad therefore icreasig desity. Secodly, the potetial icrease i frequecy alog each spoke may icrease demad ad therefore also desity.. Hub Characteristics The competitie adatages of a HS system are highly depedet o the hub cities. Not just ay city ca sere as a hub airport. There are four desirable characteristics of a hub city which are: airport performace, ecoomic support, etwork coectiity, ad cetral locatio. The high-frequecy flights betwee hubs requires sufficiet traffic olume, which holds the cetral portio of a hub airport s throughput, a most reliable ad sigificat measure of the airport performace; o the other had, traffic olume is also closely related to the ecoomic situatios of the city where a airport locates. Stroger local ecoomy geerates more commercial ad busiess iteractios betwee the city ad other areas, which is a importat source of air trasportatio for
both passeger ad cargo traffic. From the study of Ji ad Wag (005), the role of tourism attractieess aloe i ifluecig the air passeger traffic is still petty; as a result it is ot our primary cocer i this paper. The coectiity form betwee a airport ad its eighborig couterparts is also importat. If may liks already exist withi the eighborig airports, regioal traelers do ot hae to pass through the studied airport, therefore weakeig the hub role of the studied airport. At last, cetral locatio is certaily preferred sice it miimizes the distace traeled o each spoke. The importace of topological ad physical trael distace may ary accordig to the actual stage legth, e.g. i short-haul air trael, passegers seem to be more cocered with the umber of trasfers. Such a cosideratio is reflected i the followig sectio. 3 The Curret Airport System i Chia ad its Problems Sice the implemetatio of the Reform ad Ope-up policy i the 970s, the ciil aiatio idustry of mailad Chia has witessed a rapid growth. By the ed of 004, there are 035 domestic flights (those from/to Hog Kog/Macao are ot icluded), ad 5586 km i terms of operatioal mileage. It raked the 3 rd amog 88 IATA members. Howeer, the airlie etwork structure is still largely remais a PP form with too much emphasis o the truk lies; whereas feeder lies do ot receie eough attetio they desere (Bai 006). Although this may be partially due to the differece of liig stadards ad social-ecoomic deelopmet betwee metropolises ad smaller cities, ad betwee easter ad wester part of the coutry, the primary reasos are from the air trasportatio system itself. Firstly, short-haul flights are uable to attract passegers from surface trasportatio such as rail ad log-distace coach trasportatio, which ca be attributed to the ucompetitie airport accessibility, much higher prices, ad the low frequecy of scheduled flights. This problem is crucial i that a strog support of short-haul feeder lies is a key poit i the success of a real HS structure. Secodly, the pheomeo that airport ifrastructure leel is higher tha eeded widely exists. Table illustrate the class distributio of all the airports i mailad Chia, from which we fid that the distributio is far less tha proportioal i formig a HS structure. This also illustrates that the air trasportatio etwork still maitais PP characteristics. Too may high-class airports oly result i a waste of costructio, operatio, ad maiteace expeses, thus affectig the global efficiecy ad competitieess of the HS system. Table Airport class distributio i mailad Chia (year: 004) Airport Type 4E 4D 4C 3C Number of Airports 5 34 5 6 Aircraft Size Max B747 B767, B757, MD8 B737 Smaller tha B737 Source: Statistical data o ciil aiatio of Chia 005 With the cotiuity of atioal ecoomic prosperity ad the cetral goermet s policy preferece, i the decades ahead the aboe regioal gaps would be greatly shorteed ad air traffic i the less-deeloped regios or cities would defiitely experiece a more remarkable icrease. It at the same time proides the Chiese mailad airport system with a ideal opportuity to accelerate its pace towards a efficiet HS etwork. To accomplish it, the first step is to cofigure the hub airports.
4 Hub Airport Plaig We cosider the selectio of a hub airport from local, regioal, ad global leels to icorporate the four desirable characteristics discussed i sectio. I the first stage we cosider the local effects of airports by employig the cluster aalysis method. The complex etwork theories are applied to measure the extet of coectiity ad cetral locatio of each airport. The fial plaig scheme is based o all the former aalysis. Details are gie as follows. 4. Local Effects I the four characteristics, airport performace ad ecoomic support are classified as the local factors. To more accurately represet their effects, the two factors are diided ito four elemets: passeger throughput, cargo throughput, local GDP, ad o-agricultural populatio, which are defied as the iput ariables for cluster aalysis. Relatie data are collected for the year 004. I the cluster aalysis we use the followig Mikowski distace to measure the similarity betwee each two airports, k = d = [ ( x x ) ] () ij ik jk where x ik ad x jk represet the kth iput ariable of the ith ad jth airports respectiely, ad d ij deotes the similarity betwee the two airports. I gaugig the similarity betwee two sample classes, Ward method is adopted: T D = ( xi x ) ( xi x ) i which there are D xi G T = ( x j x) ( x j x) x G j T D + = ( xk x) ( xk x) x G G k x = xi = xi G x j G () x x j x = x We defie the distace betwee two sample classes is, G) k 3 xk G G D( G = D + D D (3) More details ca be foud i Yag et al. (004), ad we opt to form 4, 6, ad 8 clusters successiely. Part of the results is gie i table. Simply from the local effects, we fid that the airports of Beijig, Shaghai, ad Guagzhou are i a well distict cluster, although the airport of Guagzhou is a little differet from the other two i certai cases. The airports of Shezhe, Tiajig, Chegdu, Chogqig, ad Hagzhou are ery alike. I the 3rd cluster the cities where airports are located are ot ecessarily proicial capitals; istead, may i it are ecoomically dyamic cities i the easter part of Chia. 4. Regioal Effects A airport s regioal effects capture the effect of its regioal etwork coectiity, which ca be measured by the extet of passig through that airport for a regioal trip. I the complex
etworks theories, clusterig coefficiet is used to assess the regioal effects of each ertex i the etwork. Sice the Chiese airport etwork has proe to exhibit properties of a small world, oe form of the complex etworks, the clusterig coefficiet is also employed i our study. We first simplify the airport etwork by trasformig it ito a udirected graph G (V, E) with each ertex represetig a airport ad eery edge correspodig to a route (two directios are regarded as oe i the graph) betwee two airports. The defiitio of a airport s clusterig coefficiet is as M C = (4) C where M is the umber of the real coectios withi airport s direct eighborhood N cosistig of airports, ad C is the total umber of all possible coectios amog its eighborig airports. Obiously we hae C [ 0,] δ l M ca be calculated as = 0 M. If we defie ariable if edge l is liked with otherwise = x l l E; x, y N δ l as y δ δ (6) l Figure shows the clusterig coefficiets of the first 7 airports with alues i a icreasig order. It should be oted that for the airports who hae oly oe direct lik, its clusterig coefficiet is defied as zero. They are excluded from our cosideratio. For the rest of the airports, eidetly a smaller clusterig coefficiet meas a higher regioal importace (effects) because i such a case the commuicatio amog the eighborig airports is more likely to pass through the studied airport first. Therefore i figure we use the term -clusterig coefficiet to represet the regioal effect of the airports. The domiace of Beijig, Shaghai, Guagzhou, Shezhe, ad Kumig is sigificat. The reasos for Kumig is that may Proicial tourism flights depart exclusiely from Kumig; i other words, the airport etwork i Yua already exhibit some features of a HS structure. Similar pheomeo ca be foud i Xijiag, where Urumchi plays a equialet role (Ji ad Wag 005). (5) Table Cluster Aalysis Results No. of Clusters 4 st Cluster d Cluster 3 rd Cluster Chegdu, Kumig, Xi a, Hagzhou, Qigdao, Dalia, Beijig, Guagzhou, Najig, Chogqig, Wuha, Sheyag, Harbi, Shaghai Shezhe Chagsha, Fuzhou, Zhegzhou, Wezhou, Jia Beijig, Shezhe, Tiajig, Fuzhou, Quazhou, Shijiazhuag, Zhegzhou, Harbi, 6 Shaghai, Chegdu, Chogqig, Chagchu, Dalia, Sheyag, Jia, Qigdao, Guagzhou Hagzhou Wuha, Najig, Yatai, Nigbo, Wezhou Beijig, Shezhe, Tiajig, Fuzhou, Quazhou, Shijiazhuag, Zhegzhou, Najig, 8 Shaghai, Chegdu, Chogqig, Harbi, Wuha, Chagchu, Dalia, Sheyag, Guagzhou Hagzhou Jia, Qigdao, Yatai, Nigbo, Wezhou
The passeger ad cargo throughput of Shaghai are the sum of the two airports (Hogqiao ad Pudog). Such cosideratio is also applied to the 6 ad 8 cases. I the 8 case, Shaghai is classified i a idiidual cluster which is ear to {Beijig, Guagzhou}. We regard the two as oe cluster for the sake of simplicity. 4.3 Global Effects I the four characteristics stated i sectio, cetral locatio is used to measure the global effects of a airport. It ca be reflected by the umber of the shortest routes i which the studied airport is either the origi/destiatio, or a itermediate stop. I effect, the larger the umber, the more importat the role the airport plays i shorteig trael distace oer the whole etwork. Such a cocept i complex theory is defied as betweeess, ad is calculated as the fractio of shortest paths betwee ertexes pairs that pass through the ertex of iterest. Let S ij deote the set of the shortest routes ad the airport s betweeess is defied as B = i, j E l Sij S δ ij l We employ the Floyd algorithm (Wag 993) to fid the shortest route betwee ay two airports i the etwork. Although i may istaces the high speed of air trasportatio makes passeger more cocered with trasfer tha actual stage legth, for the log-haul trips the impact of actual distace o passegers choice is more perceptible. As a result, we recostruct a weighted graph i which the weight of each edge represets the physical distace betwee two airports. Each airport s betweeess is calculated both i the weighted ad uweighted graphs. Major results are show i figure. (7) Betweeess 0.55 0.5 -Clusterig Coef. 0.45 B (physical dist.) 0.4 B (topological dist.) 0.35 0.3 0.5 0. 0.5 0. 0.05 0 Beijig Guagzhou Shaghai Shezhe Kumig Chegdu Urumchi Chagsha Xi'a Xiame Chogqig Fuzhou Qigdao Wuha Sheyag Najig Dalia Hagzhou Zhegzhou Chagchu Haikou Wezhou Tiajig Nigbo Yatai Harbi Jia Figure Results of clusterig coefficiets ad betweeess of the selected airports 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0. 0. 0 -Clusterig Coefficiet Clearly, Beijig Capital Airport ows the highest alues of betweeess with either topological or physical distace. I the topological structure, the betweeess of Beijig is followed by Kumig, Shaghai, Guagzhou, Urumchi, Shezhe, Chegdu, Xi a, ad Wuha, successiely. While the actual distaces are take ito accout, the decreasig order becomes Urumchi, Xi a, Guagzhou, Chegdu, Sheyag, Shaghai, Qigdao, Harbi, ad Wuha. The comparatiely high degree of betweeess of Urumchi, Xi a, Qigdao, ad Sheyag i the
latter case might be attributed to their geographic locatios. For example, if passegers from Chogqig fly to Hohhot, they hae to make oe trasfer sice o direct flight exists. There are seeral trasfer choices such as Beijig or Xi a. Their positios are equal proidig that oly topological coectios are cosidered. Howeer, the actual trip legth ia Xi a is much shorter because the two segmets of the trael are almost i a lie. Similar circumstaces ca be foud i trips from southeast cities to the ortheast part of the coutry where there are ot may direct air trasportatio serices. Geographically, Qigdao proides a ideal locatio for oe-stop trasfers. 4.4 Plaig Scheme of Natioal Hub Airports If we comprehesiely take ito accout the local, regioal, ad global effects of all the airports, we fid the airports i Beijig, Shaghai, ad Guagzhou are obiously predomiat i all the airports. Shezhe Airport is ery ext to them. What follows are Chegdu, Tiajig, Chogqig, ad Hagzhou i terms of local effects, Kumig, Chegdu, Urumchi, Chagsha, ad Xi a for the regioal effects, ad Urumchi, Xi a, Chegdu, Kumig, Sheyag, Qigdao, ad Wuha if we cosider global effects. The airport of Chegdu is somewhat less ifluetial tha those i Beijig, Shaghai, Guagzhou, ad Shezhe, yet its global effects are much stroger tha ay of the rest airports. Although Tiajig, Chogqig, ad Hagzhou show strog local effects largely due to their ecoomic support, they are ot icluded as primary hubs i that i their eighborhoods primary hubs already exist which are Beijig, Chegdu, ad Shaghai. For the same reaso the airport of Shezhe is ot idetified as a primary hub. Kumig, Urumchi, ad Xi a show their regioal ad global competece as well; howeer, their local effects are ot as strog as the other airports ad thus might rather sere as a hub whose mai fuctio is to proide a place for trasfers. Furthermore, the airports of Sheyag, Qigdao, ad Wuha are similar i terms of all the three aspects by holdig comprehesiely secodary positios; i additio, their geographical locatios are rather idepedet of the aboe airports: Sheyag is i the ortheast; Qigdao is located i the cetre of the orther coastal area; the distaces betwee Wuha ad its earest airports metioed aboe, e.g. Shaghai, Guagzhou, Xi a, ad Chegdu, almost equal to each other ad are approximately 800-000 km. Our aboe cosideratios ca be summarized as a prelimiary plaig scheme of the hub airports i the mailad Chia, which is show i figure. The four atioal primary airports are: Beijig Capital Airport, Shaghai Airport (Hogqiao ad Pudog are regarded as oe), Guagzhou Baiyu Airport, ad Chegdu Shuagliu Airport, who are resposible for the major trasfer tasks i the North, East, South, ad West Chia. Secodary airports iclude Urumchi, Xi a, Chogqig, Kumig, Wuha, Tiajig, Sheyag, Qigdao, Hagzhou, ad Shezhe. I a geographic sese they are eely distributed; howeer, their roles are ot exactly the same. Tiajig, Chogqig, Hagzhou, ad Shezhe sere as auxiliary hub airports of their eighborig primary hubs respectiely. I additio to accommodatig origial ad termial traffic, their fuctio could be exteded to sharig part of the passeger ad freight trasfer traffic to aoid potetial cogestio at their earby primary hubs. For the other airports, Urumchi, Xi a, Sheyag, Wuha, Qigdao, Kumig, they are expected to rather act as idepedet regioal hubs. 5 Further Discussios 5. Network Adjustmet The HS structure departs from cetralizig traffic ad promotig efficiecy of aircrafts use.
Those objecties are realized by icreasig flights frequecy betwee hubs ad strog support of feeder lies. These would, howeer, ery possibly result i potetiacl cogestio especially durig peak hours at primary hub airports. I additio to adoptig some operatioal strategies such as arrial-departure mix to form flights waes i order to alleiate this problem (Ji ad Wag 005), it is importat for plaers ad decisio-makers to ote that the startig poit of implemetig a HS etwork is to ehace global efficiecy by eadig excessie direct liks amog medium- ad small-size cities or tows, rather tha to dey the coexistece of PP structure particularly betwee large cities or proice capitals where traffic olume is substatial. Ee whe the origi ad destiatio are ot hubs, city-pair flights are still ecouraged. O the other had, the plaig of four secodary hub airports (Tiajig, Hagzhou, Shezhe, ad Chogqig) is i effect also a effort to mitigate potetial cogestio at primary hubs by switchig part of the trasfer traffic to its earby parters. Figure Hub airports i mailad Chia 5. Dyamic Eolutio With etwork deelopmet, hub airports will cotiually eole. New hubs will appear ad old oes will gradually lose its ifluece, or primary hubs will be replaced by secodary oes due to ecoomic, geographic, ad political chages. A iterestig issue is the role of Guagzhou Baiyu Airport. First, the earby Shezhe airport bears closer similarity to Baiyu Airport tha ay of its parallel airports to the rest three primary hub airports i terms of airport performace, ecoomic support, locatio, ad airlie coectiity, which poses cosiderable challeges to Baiyu Airport. Secodly, for iteratioal trasfers, Hog Kog is defiitely better tha Guagzhou for the sake of much more iteratioal scheduled flights there; o the other had, may mailad cities hae coected to Hog Kog by direct flights, the umber of which is still rapidly icreasig. As to domestic hub-ad-spoke air trael ad regioal trasfer serice withi the mailad, eertheless, Hog Kog ca ot substitute Guagzhou because of the admiistratie restraits at least i the short term. I the log ru this tred would be ery possible if restraits o loger exist ad Hog Kog ad the mailad are more closely itegrated. Furthermore, the realizatio of three exchages associated with closer social ad ecoomic iteractios betwee
the two sides of the Taiwa Straits i the log ru would defiitely exted the role of Taipei Taoyua Airport as a ew hub i the southeast Chia, i additio to its fuctio as the air trasportatio ceter of the islad. 6 Coclusios Differet from preious studies which are based o either sophisticated mathematical models or simple yet quite subjectie idex assessmet, our research gies a ew hub airport plaig process. We first fid airport performace, ecoomic support, etwork coectiity, ad cetral locatio are four desirable hub characteristics. These characteristics hae bee icorporated ito local, regioal, ad global effects by applyig cluster aalysis ad complex etwork theories to study each airport i mailad Chia. The airports i Beijig, Shaghai, Guagzhou, ad Chegdu are proposed as atioal primary hubs that are resposible for atioal major trasfer tasks. Tiajig, Hagzhou, Chogqig, Shezhe, Sheyag, Qigdao, Xi a, Urumchi, Wuha, ad Kumig are defied as secodary hubs. Their role is i geeral accommodatig local trasfer traffic i additio to city-pair flights betwee itself ad other major cities. Tiajig, Hagzhou, Chogqig, ad Shezhe ca furthermore sere as auxiliary airports of primary hubs maily owig to their geographic positios. Part of the trasfer traffic ca be switched from the primary hubs to these airports, which help aoid potetial cogestio problems at primary hub airports. Alog the route where traffic olume is sigificat, city-pair flights are still ecouraged. Hub airports is eer static. New hubs ca replace old oes; it is also possible for secodary hubs to substitute primary oes. I particular, Guagzhou Baiyu Airport faces cosiderable challeges from that of Shezhe. For foreig/domestic trasfers, Hog Kog is a better place, although for domestic ad regioal trasfers, Hog Kog airport is curretly powerless due to admiistratie barriers. With the realizatio of three exchages, Taipei Taoyua Airport is ery likely to become a ew hub of southeast Chia i the log ru. Some aspects of our studies desere further work. I the plaig process, the clusterig coefficiet is used to measure a airport s regioal effects. Howeer, the two cocepts sometimes do ot totally oerlap. It might be more precise if certai physical distace limitatios are itroduced to judge whether the airport which has a direct lik with the studied oe really belog to its eighborhood. Moreoer, how to add iteratioal coectios i the cosideratio would also be a iterestig area of future research. 7 Ackowledgemet This paper is supported by the key project of Chiese Miistry of Educatio (No. 0433). The authors would like to exted their gratitude to ZHOU Qia ad PENG Hu for their cotributio to improig our work. We also thak the aoymous referees for their costructie ad helpful commets. Refereces Ayki T. (990) O a quadratic iteger program for the locatio of iteractig hub facilities. Europea Joural of Operatioal Research, Vol. 46, No. 3, 409-4. Bagler Gaesh (004) Aalysis of the Airport Network of Idia as a Complex Weighted Network. arxi: cod-mat/0409773
Bai, M.G. et al. (006) Desig ad Applicatio of Hub ad Spoke Network. System Egieerig, Vol. 4, No. 5, 9-34. Campbell, J.F. (996) Hub Locatio ad the p-hub Media Problem. Operatio Research 44, 93-935. Chi, L.P. et al. (003) Structural Properties of US Flight Network. Chiese Physics Letters, Vol. 0, No. 8, 393-396. Erst, A.T. (996) Efficiet Algorithm for the ucapacitated Sigle Allocatio p-hub Media Problem. Locatio Sciece, 4, 39-54. Erst, A.T., Krishamoorthy M. (998) Exact ad Exact Algorithms for the ucapacititated Multiple Allocatio p-hub Media Problem. Europea Joural of Operatioal Research, 04, 00-. Guimera, R., Amaral L.A.N. (004) Modelig the World-wide Airport Network. Europea Physical Joural B, 38:38-385 Ji, F.J., (00) A Study o Network of Domestic Air Passeger Flow i Chia. Geographical Research, Vol. 0, No., 3-39. Ji, F.J., Wag, C.J. (005) Hub-ad-Spoke System ad Chia Aiatio Network Orgaizatio. Geographical Research, Vol. 4, No. 5, 774-784. Kaafai, Adib, Atef A. Ghobrial (985) Airlie Hubbig Some Implicatio s for Airport Ecoomics. Trasportatio Research A (geeral), Vol. 9, 5-7. Klicewicz, J.G. (99) Heuristics for the p-hub locatio problem. Europea Joural of Operatioal Research, Vol. 53, No., 5-37. Li, W., Cai, X. (004) Statistical Aalysis of Airport Network of Chia. Physical Reiew E 69, 04606 Morriso, Stee, Clifford Wisto (986) The Ecoomic Effects of Airlie Deregulatio. Washigto, D.C.: The Brookigs Istitutio. O Kelly, M.E. (987) A Quadratic Iteger Program for the Locatio of Iteractig Hub Facilities. Joural of Operatioal Research, E 35, 5-39. Oum, Tae H., Michael W. Tretheway (987) Airlie Hub ad Spoke Systems. workig paper, Faculty of Commerce, Uiersity of British Columbia, Vacouer. Schitler L. A., Kulkari Rajedra (00) Measurig Small-World Coectiity i Air Trasportatio Networks. Proceedigs of the 5th Iteratioal Coferece o Techology, Policy ad Ioatio: Critical Ifrastructures. Wag. Y.X. (993) Operatios Research Plaig Theories ad Network. Tsighua Uiersity Press, Beijig. Yag, H. et al. (004) Mathematical Statistics. Higher Educatio Press, Beijig. Zhag, H.M. (000) Prerequisite of Hub-Spoke System. Iteratioal Aiatio, 000.6, 37-39.